The former Tory chairman said the vote gave anyone outraged by MPs' abuse of expenses an 'ideal opportunity' to send a message to all three main parties by not voting for any of them.
The call from a senior party grandee is an extraordinary challenge to David Cameron's authority in the run-up to the June 4 poll.
In an interview with the Daily Mail, 78-year-old Lord Tebbit said it was clear that Labour, Conservative and Liberal Democrat MPs had been behaving like 'welfare junkies' addicted to abusing their Commons allowances.
'Local elections, the great British public should treat just as normal,' he said. 'But at the European elections, in my judgment they should send a very sharp message to the leaders of the three national parties by not voting for any of the national party candidates.'
Norman Tebbit, who was one of Margaret Thatcher's closest allies, refused to say which of the smaller parties he believed voters should back.
'I wouldn't seek to give any advice on that,' he said. 'But if there was an enormous fall in the vote for the major parties, the message might get through.'
Lord Tebbit did say that he would urge the public not to support the 'socialist' British National Party, which he described as 'Labour with racism'.